Consider the line L(t)=⟨5+t,1+5t⟩. Then:
Choose perpendicular, parallel or neither. (PS. Answers below may not be true.)

Answer:

Hello,

Answer 2

Step-by-step explanation:

7=2*0+7

9=2*1+7

11=2*2+7

13=2*3+7

15=2*4+7

17=2*5+7

y=2*x+7

An other way:

[tex]points\ ( 0,7)\ and\ (1,9)\\\\\Delta\ y=9-7=2\\\Delta\ x=1-0=1\\\\\\y-7=(x-0)*2\\\\y=2x+7\\[/tex]

The complete equation is [tex]y = 2x+7[/tex].

An equation is a condition on a variable such that two expressions in the variable should have equal value.

Substitution means replacing the variables (letters) in an algebraic expression with their numerical values.

According to the question.

We have a table which shows the relation between x and y.

Let the missing term be a and b.

The the given equation becomes

[tex]y = ax + b[/tex]

For finding the value of a and b.

Substitute x = 0 and y = 7 in equation y = ax + b.

[tex]\implies 7 = a(0) + b\\\implies b = 7[/tex]

Again, substitute  x = 1 and y = 9 in the equation y = ax+ b

[tex]\implies 9 = a(1) +b\\\implies 9 = a + 7\\\implies a = 2[/tex]

substitute the value of a and b in the equation y = ax + b.

[tex]\implies y = 2x+ 7[/tex]

Therefore, the complete equation is [tex]y = 2x+7[/tex].

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Answer: x=8/3 or x= 2.6666....

Step-by-step explanation:

[tex]2+3x-10=0[/tex]

[tex]2-10=-8[/tex]

[tex]3x-8=0[/tex]

add 8 on both sides

[tex]3x-8+8=0+8[/tex]

[tex]3x=8[/tex]

divide 3 on both sides

[tex]x=\frac{8}{3}[/tex]

Answer:

8/3

Step-by-step explanation:

2 +3x + 10 = 0

2-10 +3x = 0

-8 + 3x = 0

3x = 8

x = 8/3

Answer:

[tex]\boxed{\sf C. \ 10}[/tex]

Step-by-step explanation:

[tex]\sf The \ intersecting \ chord \ theorem \ states \ that \ the \ products[/tex]

[tex]\sf of \ the \ lengths \ of \ the \ line \ segments \ on \ each \ chord \ are \ equal.[/tex]

[tex]NH \times HT = MH \times HY[/tex]

[tex](x+20) \times 8=12 \times 20[/tex]

[tex]\sf Expand \ brackets \ and \ multiply.[/tex]

[tex]8x+160=240[/tex]

[tex]\sf Subtract \ 160 \ from \ both \ sides.[/tex]

[tex]8x+160-160=240-160[/tex]

[tex]8x=80[/tex]

[tex]\sf Divide \ both \ sides \ by \ 8.[/tex]

[tex]\displaystyle \frac{8x}{8} =\frac{80}{8}[/tex]

[tex]x=10[/tex]

The value of x is 10.

We have a circle and inside it two chords MY and NT intersect at point H.

We have to find the value of x in the figure.

According to the intersecting chord theorem, when two chords say AB and CD intersect at point O, then

AO x OB = CO x OD

Applying the chord intersecting theorem to the figure in the question, we get -

MH x HY = NH x HT

12 x 20 = (x+20) x 8

240 = 8x + 160

8x = 80

x = 10

Hence the value of x is 10.

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Answer:

The resultant expression is [tex]2x^{2}+5x^{2}-x-6[/tex].

Step-by-step explanation:

The distributive property of multiplication is:

[tex]a\times (b+c)=(a\times b)+(a\times c)[/tex]

The two polynomials provided are:

[tex](2x+3)\\(x^{2}+x-2)[/tex]

Determine the final expression by multiplying the two polynomials as follows:

[tex](2x+3)\times (x^{2}+x-2)=[2x\times(x^{2}+x-2)]+[3\times(x^{2}+x-2)][/tex]

[tex]=[(2x\times x^{2})+(2x\times x)-(2x\times 2)]+[(3\times x^{2})+(3\times x)-(3\times 2)]\\\\=[2x^{3}+2x^{2}-4x]+[3x^{2}+3x-6]\\\\=2x^{3}+2x^{2}+3x^{2}-4x+3x-6\\\\=2x^{3}+5x^{2}-x-6[/tex]

Thus, the resultant expression is [tex]2x^{2}+5x^{2}-x-6[/tex].

Look at the screenshot!!!

Answer:

A=108 cm²

Step-by-step explanation:

length (l)=3w

perimeter=2l+2w

P=2(3w)+2w

48=6w+2w

width=48/8

w=6

l=3w=3(6)=18

Area=l*w

A=18*6

A=108 cm²

Answer:

6 1/8th cups in 3/4 cups

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

you convert 3/4 into 8ths which will be 6/8

Answer:

Tom, 10.25

Step-by-step explanation:

Distance covered by Tom=4.5*(4 1/2+5)=81/4=42.75km

Distance covered by Jerry=6.5*(5)=32.5km

Tom is ahead from Jerry by 10.25km

9514 1404 393

Answer:

  OBADR

Step-by-step explanation:

The first two letters are swapped, and the last two letters are swapped.

  BOARD . . . becomes

  OBADR

Answer:

-2a - 3

Step-by-step explanation:

bº equals 1 due to the zero exponent.

Thus, -2a-3 bº simplifies to -2a - 3.

Answer:

−2/a^3  

Step-by-step explanation:

Answer:

718.75ft³

Step-by-step explanation:

Rectangular Prism=5x5x17.5=437.5

Cube=5x5x5=125

Triangular Prism=5x5x12.5x.5=156.25

437.5+125+156.25=718.75ft³

Answer:

Z= 0.253

Z∝/2 = ± 1.96

Step-by-step explanation:

Formulate the null and alternative hypotheses as

H0 : u1= u2 against Ha : u1≠ u2 This is a two sided test

Here ∝= 0.005

For alpha by 2 for a two tailed test Z∝/2 = ± 1.96

Standard deviation = s= 15

n= 10

The test statistic used here is

Z = x- x`/ s/√n

Z= 2058- 2046 / 15 / √10

Z= 0.253

Since the calculated value of Z= 0.253 falls in the critical region we reject the null hypothesis.

There is  evidence at the 0.05 level that the doors are too short and unusable.

no te puedo contestarte yo no hablo inglés

Answer:

Solution : 8i

Step-by-step explanation:

We can use the trivial identities cos(π / 2) = 0, and sin(π / 2) = 1 to solve this problem. Let's substitute,

[tex]8\left[cos\left(\frac{\pi }{2}\right)+isin\left(\frac{\pi \:}{2}\right)\right][/tex] = [tex]8\left(0+1i\right)[/tex]

And of course 1i = i, so we have the expression 8(0 + i ). Distributing the " 8, " 8( 0 ) = 0, and 8(i) = 8i, making the fourth answer the correct solution.

Answer:

  a) position 22

  b) 26

  c) shuffle 25

Step-by-step explanation:

Assuming the shuffling occurs so that the bottom card of the top half of the deck (card 26) becomes the bottom card (card 52), while the top card of the bottom half (card 27) becomes the top card (card 1), the sequence of card 1 positions with successive shuffles is ...

  {2, 4, 8, 16, 32, 11, 22, 44, 35, 17, 34, 15, 30, 7, 14, 28, 3, 6, 12, 24, 48, 43, 33, 13, 26, 52, 51, 49, 45, 37, 21, 42, 31, 9, 18, 36, 19, 38, 23, 46, 39, 25, 50, 47, 41, 29, 5, 10, 20, 40, 27, 1}

That is, after the first shuffle, card 1 is at position 2; after the second shuffle, it is at position 4; and so on.

(a) Hence the position of card 1 after the 7th shuffle is 22.

__

(b) The top card is in position 52 after 26 shuffles.

__

(c) The top card is in position 26 after 25 shuffles; the bottom card is in position 27 after 25 shuffles. That is when they first touch. (They touch again after 51 shuffles.)

Answer:

5%

Step-by-step explanation:

so, for 3 questions he has a 1 in 4 chances to get it right.

4³ chances, so a 1/4³ probability.

and he has one other question with a 3 in 4 chance to get it wrong.

a 3/4 probability.

that is in total

1/4³ × 3/4 = 3/4⁴

and now we have 4 over 3 combinations as possibilities to get 3 right and 1 wrong.

that is 4! / (3! × (4-3)!) = 4

so our total probability is

4 × 3/4⁴ = 3/4³ = 3/64 ≈ 0.05 = 5%

in other words, the expected quote for him to achieve that result is in 5 out of 100 (or 1 out of 20) attempts.

Answer:

∛18 * ∛18 * 18/(∛18)²

Step-by-step explanation:

Let the surface area of the box be expressed as S = 2(LB+BH+LH) where

L is the length of the box = x

B is the breadth of the box = x

H is the height of the box = h

Substituting this variables into the formula, we will have;

S = 2(x(x)+xh+xh)

S = 2x²+2xh+2xh

S = 2x² + 4xh and the Volume V = x²h

If V = x²h; h = V/x²

Substituting h = V/x² into the surface area will give;

S = 2x² + 4x(V/x²)

Since the volume V = 18cm³

S = 2x² + 4x(18/x²)

S =  2x² + 72/x

Differentiating the function with respect to x to get the minimal point, we will have;

dS/dx = 4x - 72/x²

at dS/dx = 0

4x - 72/x² = 0

- 72/x² = -4x

72 = 4x³

x³ = 72/4

x³  = 18

[tex]x = \sqrt[3]{18}[/tex]

Critical point is at [tex]x = \sqrt[3]{18}[/tex]

If x²h = 18

(∛18)²h =18

h = 18/(∛18)²

Hence the dimension is  ∛18 * ∛18 * 18/(∛18)²

Answer:

20.8 hours

Step-by-step explanation:

Given that hours (h) varies inversely with age (a) then the equation relating them is

h = [tex]\frac{k}{a}[/tex] ← k is the constant of variation

To find k use the condition h = 52 when a = 20, thus

52 = [tex]\frac{k}{20}[/tex] ( multiply both sides by 20 )

1040 = k

h = [tex]\frac{1040}{a}[/tex] ← equation of variation

When a = 50, then

h = [tex]\frac{1040}{50}[/tex] = 20.8 hours

Step-by-step explanation:

F(n)=|sin(n)|+|sin(n+1)|

then

F(n+π)=|sin(n+π)|+|sin(n+π+1)|=|sin(n)|+|sin(n+1)|=F(n)

and

F(π−n)=|sin(π−n)|+|sin(π−n+1)|=|sinn|+|sin(n−1)|≠F(n)

so we must prove when n∈(0,π), have

F(n)>2sin12

when n∈(0,π−1),then

F(n)=sinn+sin(n+1)=sinn(1+cos1)+sin1cosn

and n∈(π−1,π),then

F(n)=sinn−sin(n+1)

How prove it this two case have F(n)>2sin12? Thank you

and I know this well know inequality

|sinx|+|sin(x+1)|+|sin(x−1)|≥2sin1,x∈R

Step-by-step explanation:

Pythagoras Theorem

If the sum of the squares of the smaller two sides is equal to the square if the third side then it is a right triangle

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

So, (5)^2 + (12)^2

is 25 + 144 = 169

Which is equal to (13)^2 which is also 169

The sides of the given triangle follows pythagoras theorem, therefore it is a right triangle

Hope it helps:)

Answer:

Pythagorean theorem

Step-by-step explanation:

We can explain it using  the Pythagorean theorem. Right triangles always have a hypotenuse which is the longest side. That means 13 must be the hypotenuse of the triangle. The Pythagorean theorem is a^2+b^2=c^2

We already know all the values since every side is given so we just fill it in.

5^2+12^2=13^2

25+144=169

169=169

It is a right triangle

Recall that

tan(x) = sin(x)/cos(x)

and

sin(x) = x - x ³/6 + x ⁵/120 - x ⁷/5040 + …

cos(x) = 1 - x ²/2 + x ⁴/24 - x ⁶/720 + …

Truncate the series to three terms. Then

[tex]\displaystyle \lim_{x\to0}\frac{\tan(x)-x}{x^3} = \lim_{x\to0}\frac{\frac{x-x^3/6+x^5/120}{1-x^2/2+x^4/24}-x}{x^3} \\\\ = \lim_{x\to0}\left(\frac{x-x^3/6+x^5/120}{x^3-x^5/2+x^7/24}-\frac1{x^2}\right) \\\\ = \lim_{x\to0}\left(\frac{1-x^2/6+x^4/120}{x^2-x^4/2+x^6/24}-\frac1{x^2}\right) \\\\ = \lim_{x\to0}\left(\frac{1-x^2/6+x^4/120}{x^2\left(1-x^2/2+x^4/24\right)}-\frac1{x^2}\right) \\\\ = \lim_{x\to0}\left(\frac{1-x^2/6+x^4/120}{x^2\left(1-x^2/2+x^4/24\right)}-\frac{1-x^2/2+x^4/24}{x^2\left(1-x^2/2+x^4/24\right)}\right) \\\\ = \lim_{x\to0}\frac{x^2/3-x^4/30}{x^2\left(1-x^2/2+x^4/24\right)} \\\\ = \lim_{x\to0}\frac{1/3-x^2/30}{1-x^2/2+x^4/24} = \boxed{\frac13}[/tex]

Answer:

it is clear that at 95% confidence that the bonus plan has increased the sales significantly, because if we observe you will notice that sales after is greater than sales before in all six cases.

Step-by-step explanation:

A 95% confidence interval as we have above is the range of values that we can say with utmost certainty and confidence that 95% chance it contains the true mean of the population. in other words we can say that a  95% confidence interval defines a range of values that you can be 95% certain contains the population mean.

Answer:

149 degrees

Step-by-step explanation:

This shape is a cyclic, so opposite angles add up to 180 degrees.

180-31 = 149

Answer:

11.3 ft high

Step-by-step explanation:

Pythagorean Theorem: a² + b² = c²

4² + b² = 12²

16 + b² = 144

b² = √128

b = 11.3

Answer: g = w + 8    g=w-2

Step-by-step explanation:

We could represent the word phrases by the equations.

g = w + 8  

g = w - 2  

Answer:

g = w + 8

g = w - 2

Step-by-step explanation:

Assuming that g and w exists, then we can show the relation as described:

"Variable g is 8 more than variable w."

g = w + 8

"Variable g is also 2 less than w."

g = w - 2

These are the two equations of the described relationship between g and w.

Note that g could not actually exist in the real number system:

g = w + 8

g = w - 2

w + 8 = w - 2

w - w = -2 - 8

0 != -10

This is impossible within the real number system.

Cheers.

Answer:

sine and tangent

will be positive.

Answer:

100 times everything.

Step-by-step explanation:

If the cow is 100 times larger than its normal size, obviously everything else should be 100 times stronger and heavier.

Answer:

C=x (x+3)

Step-by-step explanation:

x cannot divide x+3 definitely so the denominators must be multiplied to get the least common denominator.

[tex]\displaystyle\\(a+b)^n\\T_{r+1}=\binom{n}{r}a^{n-r}b^r\\\\\\(x+2)^7\\a=2x\\b=3\\r+1=4\Rightarrow r=3\\n=5\\T_4=\binom{5}{3}\cdot (2x)^{5-3}\cdot3^3\\T_4=\dfrac{5!}{3!2!}\cdot 4x^2\cdot27\\T_4=\dfrac{4\cdot5}{2}\cdot 4x^2\cdot27\\\\T_4=1080x^2[/tex]

Answer:

A typical example would be when a statistician wishes to estimate the ... by the standard deviation ó) is known, then the standard error of the sample mean is given by the formula: ... The central limit theorem is a significant result which depends on sample size. ... So, the sample mean X/n has maximum variance 0.25/ n.

Step-by-step explanation: